Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Kisfaludi-Bak, Sándor https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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URN: urn:nbn:de:0030-drops-122135
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A Quasi-Polynomial Algorithm for Well-Spaced Hyperbolic TSP

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Abstract

We study the traveling salesman problem in the hyperbolic plane of Gaussian curvature -1. Let α denote the minimum distance between any two input points. Using a new separator theorem and a new rerouting argument, we give an n^{O(log² n)max(1,1/α)} algorithm for Hyperbolic TSP. This is quasi-polynomial time if α is at least some absolute constant, and it grows to n^O(√n) as α decreases to log² n/√n. (For even smaller values of α, we can use a planarity-based algorithm of Hwang et al. (1993), which gives a running time of n^O(√n).)

BibTeX - Entry

@InProceedings{kisfaludibak:LIPIcs:2020:12213,
  author =	{S{\'a}ndor Kisfaludi-Bak},
  title =	{{A Quasi-Polynomial Algorithm for Well-Spaced Hyperbolic TSP}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{55:1--55:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Sergio Cabello and Danny Z. Chen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12213},
  URN =		{urn:nbn:de:0030-drops-122135},
  doi =		{10.4230/LIPIcs.SoCG.2020.55},
  annote =	{Keywords: Computational geometry, Hyperbolic geometry, Traveling salesman}
}

Keywords: Computational geometry, Hyperbolic geometry, Traveling salesman
Seminar: 36th International Symposium on Computational Geometry (SoCG 2020)
Issue date: 2020
Date of publication: 08.06.2020


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